Development of a fully-partitioned PFEM-FEM approach for fluid-structure interaction problems characterized by free surfaces, large solid deformations, and strong added-mass effects

Fluid-Structure Interaction (FSI) phenomena are encountered in many engineering
applications and there is nowadays an increasing need for powerful numerical tools
capable to efficiently model them. In this work we address some critical features of
the numerical simulation of such problems.
In particular, the presence of free surfaces and of large solid displacements inside the
fluid flow represents a major difficulty for traditional numerical approaches, often
based on an Eulerian description of the fluid motion. The use of a Lagrangian approach
for both the fluid and the solid parts allows to take these aspects into account
in a natural way. However, in order to cope with mesh distortion issues typical of
mesh-based Lagrangian approaches, a fairly recent meshless particle method, called
Particle Finite Element Method (PFEM), has been implemented in a brand-new code
and employed in this work to model the fluid. In the context of PFEM, a novel way
to impose free-slip boundary conditions for moving boundaries of arbitrary geometry
has also been developed during this PhD.
The fluid and the solid solutions are then coupled through a fully partitioned approach,
which allows to exploit all the features of the coupled solvers at their best.
In particular, in this thesis the nonlinear Finite Element code Metafor, developed by
the MN2L lab of the University of Liège, is used to model the solid part. Thanks to
the use of a fully partitioned approach, all the nonlinear capabilities of Metafor, as
for instance the contact management and the use of complex constitutive behaviors,
are readily available. The coupling is made through CUPyDO, an integrated Python
environment for FSI coupling developed from scratch during this PhD together with
David Thomas, a researcher of the MTFC lab of the University of Liège. CUPyDO
is able to couple virtually any solid and fluid solver and provides built-in advanced
coupling strategies, and conjugate heat transfer, non-matching meshes and parallel
capabilities.
The main drawback of using a partitioned approach is that the asynchronous solution
of the solid and fluid equations may induce numerical instabilities known as
added mass effects. These effects become critical when the solid and fluid densities
are close to each other. To cure this problem while preserving a fully partitioned
approach, the Interface Quasi-Newton Inverse Least Squares (IQN-ILS) strategy has
been used in this work to perform the PFEM-FEM coupling.
Finally, the techniques developed during this PhD have been applied to the simulation
of bird strike events on aeronautical structures, providing encouraging, though
still preliminary, results.